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• W2950874560 abstract "The $R$-boundedness of certain families of vector-valued stochastic convolution operators with scalar-valued square integrable kernels is the key ingredient in the recent proof of stochastic maximal $L^p$-regularity, $2<p<infty$, for certain classes of sectorial operators acting on spaces $X=L^q(mu)$, $2le q<infty$. This paper presents a systematic study of $R$-boundedness of such families. Our main result generalises the afore-mentioned $R$-boundedness result to a larger class of Banach lattices $X$ and relates it to the $ell^{1}$-boundedness of an associated class of deterministic convolution operators. We also establish an intimate relationship between the $ell^{1}$-boundedness of these operators and the boundedness of the $X$-valued maximal function. This analysis leads, quite surprisingly, to an example showing that $R$-boundedness of stochastic convolution operators fails in certain UMD Banach lattices with type $2$." @default.
• W2950874560 created "2019-06-27" @default.
• W2950874560 creator A5031275042 @default.
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• W2950874560 date "2014-04-13" @default.
• W2950874560 modified "2023-09-27" @default.
• W2950874560 title "On the R-boundedness of stochastic convolution operators" @default.
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• W2950874560 hasPublicationYear "2014" @default.
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